The present invention relates to a new and distinct Blackberry cultivar designated ‘DrisBlackTwo’ and botanically known as Rubus L. subgenus Rubus. This new Blackberry variety was discovered in Santa Cruz County, Calif. in July 2004 and originated from a cross between the female parent Blackberry plant ‘BH936-6’ (unpatented) and the male parent Blackberry plant ‘Driscoll Cowles’ (U.S. Plant Pat. No. 14,780). The original seedling of the new cultivar was asexually propagated at a nursery in Santa Cruz County, Calif. ‘DrisBlackTwo’ was subsequently asexually propagated and underwent further testing at a nursery in Santa Cruz County, Calif. for five years. The present invention has been found to be stable and reproduce true to type through successive asexual propagations.